nuclear magnetic resonance (nmr)
DESCRIPTION
Nuclear Magnetic Resonance (NMR). Probe the Composition, Structure, Dynamics and Function of the Complete Range of Chemical Entities: from small organic molecules to large molecular weight polymers and proteins. One of the MOST Routinely used Analytical Techniques. Common NMR Utility. - PowerPoint PPT PresentationTRANSCRIPT
Nuclear Magnetic Resonance (NMR)Nuclear Magnetic Resonance (NMR)
Probe the Composition, Structure, Dynamics and Probe the Composition, Structure, Dynamics and Function of the Complete Range of Chemical Function of the Complete Range of Chemical Entities: from small organic molecules to large Entities: from small organic molecules to large molecular weight polymers and proteins. molecular weight polymers and proteins.
One of the One of the MOSTMOST Routinely used Analytical Routinely used Analytical Techniques Techniques
• Structural (chemical) elucidation
• Natural product chemistry.
• Synthetic organic chemistry. Analytical tool of choice of synthetic chemists.
• Study of dynamic processes
• Reaction kinetics.
• Study of equilibrium (chemical or structural).
• Structural (three-dimensional) studies
• Proteins.
• DNA. Protein/DNA complexes
• Polysaccharides
• Drug design
• Structure Activity Relationships by NMR
• Medicine - MRI
Common NMR UtilityCommon NMR Utility
2-phenyl-1,3-dioxep-5-ene2-phenyl-1,3-dioxep-5-ene
1313C NMR spectraC NMR spectra
11H NMR spectraH NMR spectra
NMRNMR: “fingerprint” of the compound’s chemical structure: “fingerprint” of the compound’s chemical structure
Protein Structures from NMRProtein Structures from NMR
2D NOESY Spectra at 900 MHz2D NOESY Spectra at 900 MHz Lysozyme Ribbon DiagramLysozyme Ribbon Diagram
1937 Rabi predicts and observes nuclear magnetic resonance1946 Bloch, Purcell first nuclear magnetic resonance of bulk sample1953 Overhauser NOE (nuclear Overhauser effect)1966 Ernst, Anderson Fourier transform NMR1975 Jeener, Ernst 2D NMR1985 Wüthrich first solution structure of a small protein (BPTI)
from NOE derived distance restraints1987 3D NMR + 13C, 15N isotope labeling of recombinant proteins
(resolution)1990 pulsed field gradients (artifact suppression)1996/7 new long range structural parameters:
- residual dipolar couplings from partial alignment in liquid crystalline media
- projection angle restraints from cross-correlated relaxation
TROSY (molecular weight > 100 kDa)Nobel prizes1944 Physics Rabi (Columbia)1952 Physics Bloch (Stanford), Purcell (Harvard)1991 Chemistry Ernst (ETH)2002 Chemistry Wüthrich (ETH)2003 Medicine Lauterbur (University of Illinois in Urbana ), Mansfield (University of Nottingham)
NMR HistoryNMR History
Some Suggested NMR ReferencesSome Suggested NMR References
“Basic One- and Two-Dimensional NMR Spectroscopy” Horst Friebolin
“Modern NMR Techniques for Chemistry Research” Andrew E. Derome
“NMR and Chemistry- an introduction to the fourier transform-multinuclear era” J. W. Akitt
“Nuclear Magnetic Resonance Spectroscopy” R. K Harris
“Protein NMR Spectroscopy: Principals and Practice” John Cavanagh, Arthur Palmer, Nicholas J. Skelton, Wayne Fairbrother
“NMR of Proteins and Nucleic Acids” Kurt Wuthrich
“Tables of Spectral Data for Structure Determination of Organic Compounds”Pretsch, Clerc, Seibl and Simon
“Spectrometric Identification of Organic Compounds” Silverstein, Bassler and Morrill
The Basics of NMR Hypertext based NMR course http://www.cis.rit.edu/htbooks/nmr/nmr-main.htm
Educational NMR Software All kinds of NMR softwarehttp://www.york.ac.uk/depts/chem/services/nmr/edusoft.html
NMR Knowledge Base A lot of useful NMR linkshttp://www.spectroscopynow.com/
NMR Information Server News, Links, Conferences, Jobshttp://www.spincore.com/nmrinfo/
Technical Tidbits Useful source for the art of shimminghttp://www.acornnmr.com/nmr_topics.htm
BMRB (BioMagResBank) Database of NMR resonance assignmentshttp://www.bmrb.wisc.edu/
Some NMR Web SitesSome NMR Web Sites
Basic NMR SpectrometerBasic NMR Spectrometer
Information in a NMR SpectraInformation in a NMR Spectra
1) Energy E = h
h is Planck constant is NMR resonance frequency 10-10 10-8 10-6 10-4 10-2 100 102
wavelength (cm)
-rays x-rays UV VIS IR -wave radio
ObservableObservable NameName QuantitativeQuantitative InformationInformation
Peak position Chemical shifts () (ppm) = obs –ref/ref (Hz) chemical (electronic)
environment of nucleus
Peak Splitting Coupling Constant (J) Hz peak separation neighboring nuclei (intensity ratios) (torsion angles)
Peak Intensity Integral unitless (ratio) nuclear count (ratio) relative height of integral curve T1 dependent
Peak Shape Line width = 1/T2 molecular motion peak half-height chemical exchange
uncertainty principaluncertainty in
energy
Source of the NMR SignalSource of the NMR Signal
From Quantum Theroy: Nuclear Spin (Think Electron Spin)
NMR “active” Nuclear Spin (I) = ½: 1H, 13C, 15N, 19F, 31P biological and chemical relevance Odd atomic mass
NMR “inactive” Nuclear Spin (I) = 0:12C, 16O Even atomic mass & number
Quadrupole Nuclei Nuclear Spin (I) > ½:
14N, 2H, 10B Even atomic mass & odd number
Zeeman Effect and Nuclear Spin Quantum NumberZeeman Effect and Nuclear Spin Quantum Number
I: hyperfine interaction associate with magnetization due to nuclear spin quantum transitions
Zeeman effect: splitting of energy levels in magnetic field
2I +1 possible energy levels
For I =1/2: m= -1/2 & 1/2
E= B
magnetogyric ratio (radians/Tesla) - unique value per nucleus 1H: 26.7519 x 107 rad T-1 s-1
Bo applied magnetic field - units:Tesla (Kg s-2 A-1)
NMR frequency:Bo
m: magnetic quantum number
NMR Spectra TerminologyNMR Spectra Terminology
Increasing field (Bo)Increasing frequency ()Increasing Increasing energy (E, consistent with UV/IR)
1H 13C 2H600 MHz 150 MHz 92 MHz
TMS
CHCl3
7.27 0 ppmincreasing decreasing low field high field down field up fieldhigh frequency () low frequencyde-shielding high shielding Paramagnetic diamagnetic
Another Viewpoint: Magnetic Moment (Nuclear Spin)Another Viewpoint: Magnetic Moment (Nuclear Spin)
magnetic moment()Ih
It is a vector quantity that gives the direction and magnitude (or strength) of the ‘nuclear magnet’
By convention:spin +1/2 => low energy statespin -1/2 =>
Analogous to current moving in a loop which induces a magnetic field (right-hand rule)
quantized by Planck’s constant (h)
Bo
= h / 4
Magnetic alignmentMagnetic alignment
In the absence of external field,each nuclei is energetically degenerate
Add a strong external field (Bo).and the nuclear magnetic moment: aligns with (low energy) against (high-energy)
NMR SensitivityNMR Sensitivity
Bo = 0
Bo > 0 E = h
N / N = e E / kTBoltzmman distribution:
The applied magnetic field causes an energy difference between aligned() and unaligned() nuclei
The population (N) difference can be determined from
The E for 1H at 400 MHz (Bo = 9.5 T) is 3.8 x 10-5 Kcal / mol
Very Small !Very Small !~64 excess spins ~64 excess spins per million in lower per million in lower statestate
Low energy gap
NMR SensitivityNMR Sensitivity
EhBo /2
NMR signal depends on:1) Number of Nuclei (N) (limited to field homogeneity and
filling factor)2) Gyromagnetic ratio (in practice 3)3) Inversely to temperature (T)4) External magnetic field (Bo
2/3, in practice, homogeneity)5) B1
2 exciting field strengthN / N = e E / kT
Increase energy gap -> Increase population difference -> Increase NMR signal
E ≡ Bo≡
- Intrinsic property of nucleus can not be changed.
C)3 for 13C is 64xN)3
for 15N is 1000x
1H is ~ 64x as sensitive as 13C and 1000x as sensitive as 15N !
Consider that the natural abundance of 13C is 1.1% and 15N is 0.37%relative sensitivity increases to ~6,400x and ~2.7x105x !!
signal (s) 44BBoo22NBNB11g(g()/T)/T
NMR SensitivityNMR Sensitivity
Increase in Magnet Strength is a Major Means to Increase SensitivityBut at a significant cost!
~$800,000 ~$2,00,000 ~$4,500,000
E = h = Bo / 2
E = h Bo / 2
NMR Frequency Range (NMR Frequency Range (expensive radiosexpensive radios))
For 1H in normal magnets (2.35 - 18.6 T), this frequency isin the 100-800 MHz range.
10-10 10-8 10-6 10-4 10-2 100 102
wavelength (cm)
-rays x-rays UV VIS IR -wave radio
= 2 o = B (radians)Precession or Larmor frequency:
l
angular momentum (l)
Simply, the nuclei spins about itsaxis creating a magnetic moment
Classical View of NMR (Classical View of NMR (compared to Quantum viewcompared to Quantum view))
Maxwell: Magnetic field Moving charge≡
Bo
o
Apply a large external field (Bo)and will precess about Bo at its Larmor () frequency.
Important: This is the same frequency obtained from the Important: This is the same frequency obtained from the energy transition between quantum statesenergy transition between quantum states
Bulk magnetization Bulk magnetization (M(Moo))
Mo
y
x
z
x
y
z
Bo Bo
Now consider a real sample containing numerous nuclear spins:
Mo (N - N)
xiyjzk
Since is precessing in the xy-plane, Mo = ∑ zk – zk
is quantized ( or ), Mo has a continuous number of states, bulk property.
An NMR ExperimentAn NMR Experiment
Mo
y
x
z
x
y
z
Bo Bo
We have a net magnetization precessing about Bo at a frequency of o with a net population difference between aligned and unaligned spins.
Now What?
Perturbed the spin population or perform spin gymnasticsBasic principal of NMR experiments
Mo
z
x
i
B1
Transmitter coil (y)
yBo
An NMR ExperimentAn NMR Experiment
To perturbed the spin population need the system to absorb energy.
Two ways to look at the situation: (1) quantum – absorb energy equal to difference in spin states(2) classical - perturb Mo from an excited field B1
B1 off…
(or off-resonance)
Mo
z
x
B1
z
x
Mxy
y y1
1
Right-hand rule
resonant condition: frequency (1) of B1 matches Larmor frequency (o)energy is absorbed and population of and states are perturbed.
An NMR ExperimentAn NMR Experiment
And/Or:And/Or: Mo now precesses about B1
(similar to Bo) for as long as the B1 field is applied.
Again, keep in mind that individual spins flipped up or down(a single quanta), but Mo can have a continuous variation.
An NMR ExperimentAn NMR Experiment
What Happens Next?
The B1 field is turned off and Mxy continues to precess about Bo at frequency o.
z
x
Mxy
Receiver coil (x)
y
NMR signal
o
The oscillation of Mxy generates a fluctuating magnetic field which can be used to generate a current in a receiver coil to detect the NMR signal.
FID – Free Induction Decay
NMR Signal Detection - NMR Signal Detection - FIDFID
Mxy is precessing about z-axis in the x-y plane
Time (s)
y y y
The FID reflects the change in the magnitude of Mxy as the signal is changing relative to the receiver along the y-axis
Again, it is precessing at its Larmor Frequency (o).
NMR Signal Detection - Fourier NMR Signal Detection - Fourier TransformTransform
So, the NMR signal is collected in the Time - domain
But, we prefer the frequency domain.
Fourier Transform is a mathematical procedure that transforms time domain data into frequency domain
z
x
Mxy
yBo
z
x
Mxy
yo
Laboratory Frame Rotating Frame
Laboratory Frame vs. Rotating FrameLaboratory Frame vs. Rotating Frame
To simplify analysis we convert to the rotating frame.
Simply, our axis now rotates at the Larmor Freguency (o). In the absent of any other factors, Mxy will stay on the x-axis
All further analysis will use the rotating frame.
Chemical Chemical ShiftShift
Up to this point, we have been treating nuclei in general terms.Simply comparing 1H, 13C, 15N etc.
If all 1H resonate at 500MHz at a field strength of 11.7T, NMR would not be very interesting
Beff = Bo - Bloc --- Beff = Bo( 1 - )
is the magnetic shielding of the nucleus
The chemical environment for each nuclei results in a unique local magnetic field (Bloc) for each nuclei:
Chemical Chemical ShiftShiftAgain, consider Maxwell’s theorem that an electric current in a loop
generates a magnetic field. Effectively, the electron distribution in the chemical will cause distinct local magnetic fields that will either add to or subtract from Bo
HO-CH2-CH3
Aromaticity, electronegativity and similar factors will contribute to chemical shift differences
Beff = Bo( 1 - )
de-shielding high shieldingShielding – local field opposes Bo
The NMR scale (The NMR scale (, ppm), ppm)
- ref
= ppm (parts per million) ref
Instead use a relative scale, and refer all signals () in the spectrum to the signal of a particular compound (ref).
Bo >> Bloc -- MHz compared to Hz
Comparing small changes in the context of a large number is cumbersome
Tetramethyl silane (TMS) is a common reference chemicalH3C Si CH3
CH3
CH3
IMPORTANT: absolute frequency is field dependent ( = Bo / 2)
The NMR scale (The NMR scale (, ppm), ppm)
Chemical shift is a relative scale so it is independent of Bo. Same chemical shift at 100 MHz vs. 900 MHz magnet
IMPORTANT: absolute frequency is field dependent ( = Bo / 2)
At higher magnetic fields an NMR spectra will exhibit the same chemical shifts but with higher resolution because of the higher frequency range.
Chemical Shift TrendsChemical Shift Trends
• For protons, ~ 15 ppm:
0TMS
ppm
210 7 515
Aliphatic
Alcohols, protons to ketones
Olefins
AromaticsAmidesAcids
Aldehydes
Chemical Shift TrendsChemical Shift Trends
• For carbon, ~ 220 ppm:
ppm
50150 100 80210
Aliphatic CH3,CH2, CH
Carbons adjacent toalcohols, ketones
Olefins
Aromatics,conjugated alkenes
C=O of Acids,aldehydes, esters
0TMS
C=O inketones
Predicting Chemical Shift AssignmentsPredicting Chemical Shift Assignments
Numerous Experimental NMR Data has been compiled and general trends identified
• Examples in Handout
• See also: “Tables of Spectral Data for Structure Determination of Organic Compounds” Pretsch, Clerc, Seibl and Simon
“Spectrometric Identification of Organic Compounds” Silverstein, Bassler and Morrill
• Spectral Databases: Aldrich/ACD Library of FT NMR Spectra Sadtler/Spectroscopy (UV/Vis, IR, MS, GC and NMR)
Predicting Chemical Shift AssignmentsPredicting Chemical Shift Assignments
Predict the chemical shifts of:
Benzene Shift NO2 effect NH2 effect TotalChange sign since table lists as downfield shifta 7.27 0.95 -0.75 7.47 ppmd 7.27 0.33 -0.75 6.85 ppmc 7.27 0.17 -0.24 7.20 ppmb 7.27 0.95 -0.63 7.59 ppm
From table 3-6-1 in handout:Substituent Shift relative to benzene (ppm)
ortho meta paraNO2 -0.95 -0.17 -0.33NH2 0.75 0.24 0.63
NH2
NO2
A
BC
D
Predicting Chemical Shift AssignmentsPredicting Chemical Shift Assignments
Predict the chemical shifts of:
C |C – C – C – C – C – C 2
Chemical shift is determined by sum of carbon types.From Table 3.2 in handout:
=Bs + ∑ DmAsm +SN3 +sN4 - empirical formula
S – number of directly bonded carbonsDm – number of directly bonded carbons having M attached carbonsNp – number of carbons P bonds away
2 = B2 + [1xA23+ 1xA21 ] + [1x2] + [1x2]
2 = 15.34 + [1X16.70 +1x0] + [1x-2.69] +[1x0.25] = 29.60 ppm
Coupling ConstantsCoupling Constants
Energy level of a nuclei are affected by covalently-bonded neighbors spin-states
13C
1H 1H 1H
one-bond
three-bond
I SS
S
I
I
J (Hz)
Spin-States of covalently-bonded nuclei want to be aligned.
The magnitude of the separation is called coupling constant (J) and has units of Hz.
+J/4
-J/4
+J/4
Coupling ConstantsCoupling Constants
IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei.
Multiplets consist of 2nI + 1 lines I is the nuclear spin quantum number (usually 1/2) and
n is the number of neighboring spins.
The ratios between the signal intensities within multiplets are governed by the numbers of Pascals triangle.
Configuration Peak Ratios
A 1
AX 1:1
AX2 1:2:1
AX3 1:3:3:1
AX4 1:4:6:4:1
Coupling ConstantsCoupling Constants
NMR RelaxationNMR Relaxation
After the B1 field (pulse) is removed the system needs to “relax” back to equilibrium
Mz = M0(1-exp(-t/T1))
T1 is the spin-lattice (or longitudinal) relaxation time constant.
Think of T1 as bulk energy/magnetization exchange with the “solvent”.
Please Note: General practice is to wait 5xT1 for the system to have fully relaxed.
NMR RelaxationNMR Relaxation
Mx = My = M0 exp(-t/T2)
T2 is the spin-spin (or transverse) relaxation time constant.In general: T1 T2
Think of T2 as the “randomization” of spins in the x,y-plane
Related to line-shape
Please Note: Line shape is also affected by the magnetic fields homogeneity
(derived from Hisenberg uncertainty principal)
NMR Time ScaleNMR Time Scale
Time Scale Chem. Shift ( Coupling Const. (J) T2 relaxationSlow k << A- B k << JA- JB k << 1/ T2,A- 1/ T2,B
Intermediate k = A - B k = JA- JB k = 1/ T2,A- 1/ T2,B
Fast k >> A - B k >> JA- JB k >> 1/ T2,A- 1/ T2,B
Range (Sec-1) 0 – 1000 0 –12 1 - 20
NMR time-scale refers to the chemical shift timescale.
k = (he-ho)
Exchange Rates from NMR DataExchange Rates from NMR Data
k = (o2 - e
2)1/2/21/2
k = o / 21/2
k = o2 /2(he - ho)
h – peak-width at half-height – peak frequencye – with exchangeo – no exchangef – mole fraction – chemical shift
obs = f11 + f22
f1 +f2 =1
Continuous Wave (CW) vs. Pulse/Fourier TransformContinuous Wave (CW) vs. Pulse/Fourier Transform
NMR Sensitivity Issue
A frequency sweep (CW) to identify resonance is very slow (1-10 min.)Step through each individual frequency.
Pulsed/FT collect all frequencies at once in time domain, fast (N x 1-10 sec)
Increase signal-to-noise (S/N) by collecting multiple copies of FID and averaging signal.
S/N number of scans
* =tp
NMR PulseNMR Pulse
FT
A radiofrequency pulse is a combination of a wave (cosine) of frequency o and a step function
Pulse length (time, tp)
The fourier transform indicates the pulse covers a range of frequencies
Hisenberg Uncertainty principal again: .t ~ 1/2Shorter pulse length – larger frequency envelopeLonger pulse length – selective/smaller frequency envelope
Sweep Width f ~ 1/t
NMR PulseNMR Pulse
z
x
Mxy
y
z
x
y
Mo
B1
ttp
t = * tp * B1
NMR pulse length or Tip angle (tp)
The length of time the B1 field is on => torque on bulk magnetization (B1)
A measured quantity – instrument dependent.
NMR PulseNMR Pulse
z
x
Mxy
y
z
x
y
Mo / 2
Some useful common pulses
90o
Maximizes signal in x,y-planewhere NMR signal detected
z
x
-Moy
z
x
y
Mo
180o
90o pulse
180o pulse
Inverts the spin-population.No NMR signal detected
Can generate just about any pulse width desired.
NMR Data AcquisitionNMR Data Acquisition
Collect Digital Data ADC – analog to digital converter
0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00t1 sec
SR = 1 / (2 * SW)
The Nyquist Theorem says that we have to sample at least twice as fast as the fastest (higher frequency) signal.
Sample Rate
- Correct rate, correct frequency-½ correct rate, ½ correct frequency Folded peaks!Wrong phase!
SR – sampling rate
carrier
234 233 232 231 230 229 228 227 226 225 224 223f1 ppm
Quadrature detectionQuadrature detection
Frequency of B1 (carrier) is set to center of the spectra.
• small pulse length to excite entire spectrum• minimizes folded noise
How to differentiate between peaks upfield and downfield from carrier?
carrier
If carrier is at edge of spectra, then peaks are all positive or negative relative to carrier. But excite twice as much including noise
(B1)
B
F
B
F
PH = 0
PH
= 9
0PH = 0
PH = 90
F
F
S
S
Quadrature Quadrature detectiondetection
Use two detectors 90o out of phase.
Phase of Peaksare different.
Receiver GainReceiver Gain
The NMR-signal received from the resonant circuit in the probehead needs to be amplified to a certain level before it can be handled by the computer.
The detected NMR-signals vary over a great range due to differences in the inherent sensitivity of the nucleus and the concentration of the sample.
Data Processing – Window FunctionsData Processing – Window Functions
0 0.10 0.20 0.30 0.40 0.50t1 sec
Good stuff Mostly noise
The NMR signal Mxy is decaying by T2 as the FID is collected.
Emphasize the signal and decrease the noise by applying a mathematical function to the FID
F(t) = 1 * e - ( LB * t ) – line broadening Effectively adds LB in Hz to peak
Line-widths
Sensitivity Resolution
0 0.10 0.20 0.30 0.40 0.50t1 sec
1080 1060 1040 1020 1000 980 960 940 920 900f1 ppm
0 0.10 0.20 0.30 0.40 0.50t1 sec0 0.10 0.20 0.30 0.40 0.50
t1 sec
1080 1060 1040 1020 1000 980 960 940 920 900f1 ppm
FT FT
LB = -1.0 HzLB = 5.0 Hz
Can either increase S/N or Resolution Not Both!
Increase Sensitivity Increase Resolution
NMR Data sizeNMR Data size
digital resolution (DR) as the number of Hz per point in the FID for a given spectral width.
DR = SW / SI SW - spectral width (Hz)SI - data size (points)
Remember: SR = 1 / (2 * SW)
Also: SW = 1/2DW
Dwell time DW
TD
A Number of Interdependent Values (calculated automatically)
AQ = TD * DW= TD/2SWH
Total Data Acquisition Time:
Should be long enough to allow complete delay of FID
Higher Digital Resolution requires longer acquisition times
231.40 231.39 231.38 231.37 231.36 231.35 231.34 231.33 231.32 231.31 231.30 231.29 231.28 231.27 231.26 231.25 231.24
f1 ppm
231.42 231.40 231.38 231.36 231.34 231.32 231.30 231.28 231.26 231.24 231.22 231.20f1 ppm
0 0.20 0.40 0.60 0.80 1.00 1.2 1.4 1.6 1.8 2.0 2.2t1 sec
8K data 8K zero-fill
8K FID 16K FID
Zero FillingZero Filling
Improve digital resolution by adding zero data points at end of FID
No zero-filling 8K zero-filling
MultiDimensional NMRMultiDimensional NMR
1D NMR
Up to now, we have been talking about the basic or 1D NMR experiments
More complex NMR experiments will use multiple “time-dimensions” to obtaindata and simplify the analysis.
In a 1D NMR experiment the FID acquisition time is the time domain (t1)
Multidimensional NMR experiments may also observe multiple nuclei (13C,15N) in addition to 1H.But usually detect 1H.
2D COSY (Correlated SpectroscopY): Correlate J-coupled NMR resonances
MultiDimensional NMRMultiDimensional NMR
A series of FIDs are collected where the delay between 90o pulses (t1) is incremented. t2 is the normal acquisition time.
MultiDimensional NMRMultiDimensional NMR
During the t1 time period, peak intensities are modulated at a frequency corresponding to the chemical shift of its coupled partner.
Solid line connects diagonal peaks(normal 1D spectra). The off-diagonalor cross-peaks indicate a correlationbetween the two diagonal peaks – J-coupled.
Karplus Equation – Coupling Constants Karplus Equation – Coupling Constants
Relates coupling constant toTorsional angle.
Used to solve Structures!
J = const. + 10Cos
Karplus Equation – Coupling Constants Karplus Equation – Coupling Constants
For Protein Backbones
Nuclear Overhauser Effect (NOE)Nuclear Overhauser Effect (NOE)
Interaction between nuclear spins mediated through empty space (5Ă) (like ordinary bar magnets). Important: Effect is Time-Averaged!
Give rise to dipolar relaxation (T1 and T2) and specially to cross-relaxation and the NOE effect.
the 13C signals are enhanced by a factor1 + = 1 + 1/2 . (1H)/(13C) ~ max. of 2
Perturb 1H spin populationaffects 13C spin population NOE effect
DEPT ExperimentDEPT Experiment: Distortionless Enhancement by Polarization Transfer: Distortionless Enhancement by Polarization Transfer
13C spectra is perturbed basedOn the number of attached 1H
Takes advantage of differentpatterns of polarization transfer1H-13C NOE
2D NOESY (Nuclear Overhauser Effect)2D NOESY (Nuclear Overhauser Effect)
Diagonal peaks are correlated by through-spaceDipole-dipole interaction.
NOE is a relaxation factor that builds-up duringThe “mixing-time (m)
The relative magnitude of the cross-peak is Related to the distance (1/r6) between the Protons (≥ 5Ă).
Basis for solving a Structure!
Protein NMRProtein NMR
Number of atoms in a protein makes NMR spectra complex
Resonance overlap
Isotope label protein with 13C and 15Nand spread spectra out in 3D and 4D
Protein NMRProtein NMR
How do you assign aprotein NMR spectra?
A collection of “COSY”-likeexperiments that sequentiallywalk down the proteins’ backbone
3D-NMR experiments thatRequire 13C and 15N labeledProtein sample
Detect couplings to NHDetect couplings to NH
Protein NMRProtein NMR
Assignment strategy
We know the primary sequence of the protein.
Connect the overlapping correlation between NMR experiments
Protein NMRProtein NMR
Molecular-weight Problem
Higher molecular-weight –> more atoms –> more NMR resonance overlap
More dramatic:NMR spectra deteriorate with increasingmolecular-weight.
MW increases -> correlation time increases-> T2 decreases -> line-width increases
NMR lines broaden to the point of not being detected!
With broad lines, correlations (J, NOE) become less-efficient
Protein NMRProtein NMR
How to Solve the Molecular-weight Problem?
1) Deuterium label the protein.• replace 1H with 2H and remove efficient relaxation paths• NMR resonances sharpen• problem: no hydrogens -> no NOEs -> no structure• actually get exchangeable (NH –NH) noes can augment with specific 1H labeling
2) TROSY• line-width is field dependent